{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# _Modeling of Qubit Chain_\n",
    "\n",
    "## _Simulation of few steps of quantum walk_\n",
    "\n",
    "<img src=\"images/line_qubits_site1.png\" alt=\"Qubit Chain\">\n",
    "\n",
    "<img src=\"images/line_qubits_site.png\" alt=\"Qubit Chain Shift\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Contributor\n",
    "Alexander Yu. Vlasov\n",
    "***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The initial part is similar with [previous notebook](qubit_chain_mod.ipynb), but only circuit\n",
    "for one step without measurements is implemented. Parameter `n_step` is used in next part\n",
    "of program discussed below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pprint import pprint\n",
    "import math\n",
    "import numpy as np\n",
    "\n",
    "# importing the Qiskit\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "from qiskit import Aer, execute\n",
    "# import state tomography functions\n",
    "from qiskit.tools.visualization import plot_histogram, plot_state\n",
    "\n",
    "# Definition of matchgate\n",
    "\n",
    "def gate_mu3(qcirc,theta,phi,lam,a,b):\n",
    "    qcirc.cx(a,b)\n",
    "    qcirc.cu3(theta,phi,lam,b,a)\n",
    "    qcirc.cx(a,b)\n",
    "    \n",
    "\n",
    "n_nodes = 5 \n",
    "n_step = 3\n",
    "\n",
    "# Creating Registers\n",
    "qr = QuantumRegister(n_nodes) \n",
    "cr = ClassicalRegister(n_nodes)\n",
    "\n",
    "# Creating Circuits\n",
    "qc = QuantumCircuit(qr,cr)\n",
    "\n",
    "\n",
    "# Creating of two partitions with M1' and M2\n",
    "for i in range(0,n_nodes-1,2):\n",
    "    gate_mu3(qc,math.pi, math.pi, 0, qr[i], qr[i+1])\n",
    "for i in range(1,n_nodes,2):\n",
    "    gate_mu3(qc,math.pi/2, 0, 0, qr[i], qr[i+1])\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The method used here may be applied only for simulator and \n",
    "similar with already used in a [Qiskit tutorial](https://github.com/Qiskit/qiskit-tutorial) about \n",
    "[visualization of quantum state](../../../qiskit/basics/qiskit_visualizations.ipynb).\n",
    "The `unitary_simulator` backend is used to produce $2^n \\times 2^n$ unitary matrix\n",
    "QWalk representing quantum circuit, where $n$ is `n_nodes`. \n",
    "The complex vector with $2^n$ is initialized as initial state, \n",
    "e.g., $|\\psi_0\\rangle = |00001\\rangle$.\n",
    "Multiplication of QWalk on such a vector produces final state also with $2^n$ components\n",
    "$|\\psi_1\\rangle = Q_{\\rm Walk} |\\psi_0\\rangle$. \n",
    "The density matrix $\\rho_1 = |\\psi_1\\rangle\\!\\langle\\psi_1|$ for such a state is calculated and used for Quantum Sphere.\n",
    "Unlike of real hardware the state is not destroyed due to measurement and may\n",
    "be again used as initial state $|\\psi_{k+1}\\rangle = Q_{\\rm Walk} |\\psi_k\\rangle$. \n",
    "So, the Quantum Spheres are drawn for $\\rho_k = |\\psi_k\\rangle\\!\\langle\\psi_k|$ after each step\n",
    "of quantum walk without initialization.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step =  1\n",
      "The 0th eigenvalue = 1.0000000000000004\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf58e5c5518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step =  2\n",
      "The 0th eigenvalue = 1.0000000000000009\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf591091f98>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "step =  3\n",
      "The 0th eigenvalue = 1.0000000000000013\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xf5913d3eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# execute the quantum circuit \n",
    "backend = 'unitary_simulator' # the device to run on\n",
    "\n",
    "job = execute(qc, Aer.get_backend(backend)) # Execute quantum walk \n",
    "result = job.result()\n",
    "\n",
    "\n",
    "initial_state = np.zeros(2**n_nodes)\n",
    "initial_state[1]=1.0 # state 0 = ....0000, state 1 = ...000001\n",
    "\n",
    "QWalk = result.get_data(qc)['unitary']\n",
    "\n",
    "#Applying QWalk n_step times\n",
    "for i in range(0,n_step):\n",
    "    if i > 0: initial_state = np.copy(state_QWalk) # Copy previous state\n",
    "    state_QWalk = np.dot(QWalk,initial_state)      # Multiply on QWalk matrix\n",
    "    rho_QWalk=np.outer(state_QWalk, state_QWalk.conj()) # Calculate density matrix\n",
    "    print('step = ',i+1)                           # print number\n",
    "    plot_state(rho_QWalk,'qsphere')                # draw Quantum Sphere\n",
    "    "
   ]
  },
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   "source": [
    "The method used above is possible _only for simulation_. \n",
    "Real hardware _should not_ use result of previous step altered due to measurement. \n",
    "So, for $n$ steps of walk it is necessary to make $n$ different experiments with\n",
    "`n_step`=$1,2,\\dots,n$ \n",
    "and each such attempt could include additional series of runs to provide \n",
    "[state tomography](../../../qiskit/ignis/state_tomography.ipynb)\n",
    "for whole process of quantum walk.\n"
   ]
  }
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